Displaying similar documents to “The distribution of the sum-of-digits function”

Normalizing constants for a statistic based on logarithms of disjoint m-spacings

Franciszek Czekała (1996)

Applicationes Mathematicae

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The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].

On partitions without small parts

J.-L. Nicolas, A. Sárközy (2000)

Journal de théorie des nombres de Bordeaux

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Let r ( n , m ) denote the number of partitions of n into parts, each of which is at least m . By applying the saddle point method to the generating series, an asymptotic estimate is given for r ( n , m ) , which holds for n → ∞ , and 1 ≤ m ≤ c 1 n log n c 2 .

On normal lattice configurations and simultaneously normal numbers

Mordechay B. Levin (2001)

Journal de théorie des nombres de Bordeaux

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Let q , q 1 , ⋯ , q s ≥ 2 be integers, and let α 1 , α 2 , ⋯ be a sequence of real numbers. In this paper we prove that the lower bound of the discrepancy of the double sequence ( α m q n , ⋯ , α m + s - 1 q n ) m , n = 1 M N coincides (up to a logarithmic factor) with the lower bound of the discrepancy of ordinary sequences ( x n ) n = 1 M N in s -dimensional unit cube ( s , M , N = 1 , 2 , ⋯ ) . We also find a lower bound of the discrepancy (up to a logarithmic factor) of the sequence ( α 1 q 1 n , ⋯ , α s q s n ) n = 1 N (Korobov’s problem).

On mean central limit theorems for stationary sequences

Jérôme Dedecker, Emmanuel Rio (2008)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we give estimates of the minimal 𝕃 1 distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.